Problem: Simplify the following expression and state the condition under which the simplification is valid: $k = \dfrac{p^2 + 2p}{p^2 - 4p - 12}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{p^2 + 2p}{p^2 - 4p - 12} = \dfrac{(p)(p + 2)}{(p - 6)(p + 2)} $ Notice that the term $(p + 2)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(p + 2)$ gives: $k = \dfrac{p}{p - 6}$ Since we divided by $(p + 2)$, $p \neq -2$. $k = \dfrac{p}{p - 6}; \space p \neq -2$